Teaching finance with Monte Carlo simulation

[jamalmunshi]

Some of the social sciences suffer from "physics envy". This malady causes educators to inject an unnecssary amount of mathematics into the curriculum as a way of gaining scientific letgitimacy. Sadly for most undergrads, the math actually gets in the way. I wrote a paper in which I describe the use of Monte Carlo simulation as a teaching tool in finance. The proposed teaching method greatly reduces the use of scary equations that businss undergrads hate. I would be grateful for some feedback on this idea. Here is the link to my paper:
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2512091

 

[Greg Bernhardt]

Tell us more about this "Monte Carlo simulation"

 

[jamalmunshi]

A Monte Carlo simulation is a simulated experiment. The difference between simulated and analytical solutions is best explained with a simple coin toss example. Suppose that we want to know the probability of tossing three heads in a row with a fair coin. Since the probability a fair coin coming up heads is π=0.50, the analytical solution is p(3 heads in a row) = π^3 = 0.125. In the Monte Carlo simulation for this problem we would toss a coin say ten thousand times and count the number of times that we got three heads in a row. We can simulate 10,000 coin tosses of a fair coin by taking a sample of 10,000 events from a Bernoulli distribution with π=0.50. We now have a column of 10,000 zeroes and ones in Excel. We then simply count the number of times we find three consecutive ones and when I did it I found that this occurs 1,246 times. We therefore estimate the probability of three heads in a row as 1246/10000 = 0.1246. A Monte Carlo simulation is a brute force solution that uses computational intensity as a substitute for mathematical complexity.

 

[BruceW]

I only skim-read your paper, but I like it. I agree that most students are much more comfortable with the 'frequentist' perspective of probabilities. i.e. probability tells us how frequently a certain outcome, or set of outcomes will occur. So, in this sense if the students get to explicitly run the simulation, they are in fact doing the thousand coin tosses, and counting frequency of outcomes.

On the other hand, I think the students must learn at least some of the mathematics. There is some balance that needs to be struck, and I guess your point is that the students would benefit more from more computer simulation and less of the mathematics. I think I agree when the mathematics is annoyingly long or complicated. But still I think it is important to learn the basics. For example, in your coin tossing experiment, should you count the number of times there are exactly 3 heads in a row and then a tails? Or the number of times there is a string of at least 3 heads in a row? Or the number of times that there has just previously been at least 2 heads in a row, and now you have another head? The students should at least be able to think about such problems, even if they are not fully confident with them.

 

[jamalmunshi]

Very interesting comment, HomeworkHelper. Thank you. I like the idea that there should be some balance and that the students should be given the tools to think through complicated situations. I will try to incorporate these ideas into my follow up paper which I am already working on. The problem for business professors is that most of our undergrads are not good at math and many of them just hate math. The important question is whether we can still teach them finance; and the point of my paper is that I have found a way to do that. Again thank you for your very helpful comment.

 

[pbuk]

It depends on the focus of your course. If you are aiming to give your students a superficial appreciation of some of the implications of e.g. portfolio theory, demonstrating this with a Monte Carlo simulation is fine (although an example using carefully selected actual data might be even better). However if you are aiming to give your students an understanding of portfolio theory, then you need the maths: of course this requires your students to have a certain base of mathematical skills. If they don't have these skills then there is no point showing them the maths, but there is also no hope of them truly grasping portfolio theory - at best they may gain a superficial understanding which in Physics is generally called "hand waving".

 

[jamalmunshi]

Yes, correct. Thank you for that heads up. It depends on the learning objectives. The primary target of my paper is the undergrad course in finance that all business majors must take. There are of course specialized quantitative finance courses in graduate school where the learning objectives may require a great deal of math although from what I have seen they spend more time on simulation these days too. One of the greatest mathematical moments in the history of finance was the derivation of a very beautiful option pricing model called the Black-Scholes equation. Myron Scholes received the Nobel in econ for that equation. Physics envy in finance peaked at about that time. Yet the reality is that these days Monte Carlo simulation is becoming more popular than Black-Scholes for option pricing as more innovative derivative contracts evolve. Here is a discussion among grad students in quantitative finance: http://quant.stackexchange.com/ques...n-over-analytical-methods-for-options-pricing

 

[jamalmunshi]

Here is a discussion among grad students in quantitative finance: http://quant.stackexchange.com/ques...n-over-analytical-methods-for-options-pricing

Sorry, wrong link, it is a relevant discussion but not the one among grad students that i thought i was posting.